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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cvlatcvr1 | Unicode version |
Description: An atom is covered by its join with a different atom. (Contributed by NM, 5-Nov-2012.) |
Ref | Expression |
---|---|
cvlatcvr1.j |
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cvlatcvr1.c |
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cvlatcvr1.a |
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Ref | Expression |
---|---|
cvlatcvr1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp13 989 |
. . . 4
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2 | cvlatl 29820 |
. . . 4
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3 | 1, 2 | syl 16 |
. . 3
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4 | eqid 2412 |
. . . 4
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5 | eqid 2412 |
. . . 4
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6 | cvlatcvr1.a |
. . . 4
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7 | 4, 5, 6 | atnem0 29813 |
. . 3
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8 | 3, 7 | syld3an1 1230 |
. 2
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9 | eqid 2412 |
. . . 4
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10 | 9, 6 | atbase 29784 |
. . 3
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11 | cvlatcvr1.j |
. . . 4
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12 | cvlatcvr1.c |
. . . 4
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13 | 9, 11, 4, 5, 12, 6 | cvlcvrp 29835 |
. . 3
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14 | 10, 13 | syl3an2 1218 |
. 2
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15 | 8, 14 | bitrd 245 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: cvlatcvr2 29837 atcvr1 29911 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 ax-rep 4288 ax-sep 4298 ax-nul 4306 ax-pow 4345 ax-pr 4371 ax-un 4668 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2266 df-mo 2267 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-ne 2577 df-nel 2578 df-ral 2679 df-rex 2680 df-reu 2681 df-rab 2683 df-v 2926 df-sbc 3130 df-csb 3220 df-dif 3291 df-un 3293 df-in 3295 df-ss 3302 df-nul 3597 df-if 3708 df-pw 3769 df-sn 3788 df-pr 3789 df-op 3791 df-uni 3984 df-iun 4063 df-br 4181 df-opab 4235 df-mpt 4236 df-id 4466 df-xp 4851 df-rel 4852 df-cnv 4853 df-co 4854 df-dm 4855 df-rn 4856 df-res 4857 df-ima 4858 df-iota 5385 df-fun 5423 df-fn 5424 df-f 5425 df-f1 5426 df-fo 5427 df-f1o 5428 df-fv 5429 df-ov 6051 df-oprab 6052 df-mpt2 6053 df-1st 6316 df-2nd 6317 df-undef 6510 df-riota 6516 df-poset 14366 df-plt 14378 df-lub 14394 df-glb 14395 df-join 14396 df-meet 14397 df-p0 14431 df-lat 14438 df-clat 14500 df-oposet 29671 df-ol 29673 df-oml 29674 df-covers 29761 df-ats 29762 df-atl 29793 df-cvlat 29817 |
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